Anja simplified the expression 10x^-5/-5x^10 to 15/x^15. What mistake did anja make?

Well she made the mistake of dividing the coefficient and the variable with the exponent wrong. we can look at this like

(10 * x^-5) / (-5 * x^10)

we can actually factor out the 10 and the 1/-5 ans get 2 fractions to see this clearer.

(10 / - 5) * (x^-5 / x^10)

we can clearly say

10/-5 = - 2

now the other one. when stuff that has exponents, as long as they have the same base we just subtract the exponents. so:

(x^-5 / x^10) =

x^ (-5 - 10) =

x^-15

put those 2 together

(-2) * (x^-15)

-2x^-15